Transcription

1 BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time µ is changed by vigorous exercise, so you have a random sample of nine employees of your company (that you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. It takes them an average of x = 31.2 seconds to complete the maze. Use this information to test the hypotheses H0: µ = 30, Ha: µ 30 at the 1% significance level You conclude A) that H0 should be rejected. B) that H0 should not be rejected. C) that Ha should be accepted. D) this is a borderline case and no decision should be made. 2. An agricultural researcher plants 25 plots with a new variety of corn that is drought resistant and hence potentially more profitable. The average yield for these plots is x = 150 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean µ and that a 95% confidence interval for µ is found to be 150 ± Which of the following is true? A) A test of the hypotheses H0: µ = 150, Ha: µ 150 would be rejected at the 0.05 level. B) A test of the hypotheses H0: µ = 150, Ha: µ > 150 would be rejected at the 0.05 level. C) A test of the hypotheses H0: µ = 160, Ha: µ 160 would be rejected at the 0.05 level. D) All the above. 3. A certain population follows a normal distribution with mean µ and standard deviation σ = 2.5. You collect data and test the hypotheses H0: µ = 1, Ha: µ 1. You obtain a P-value of Which of the following is true? A) A 95% confidence interval for µ will include the value 1. B) A 95% confidence interval for µ will include the value 0. C) A 99% confidence interval for µ will include the value 1. D) A 99% confidence interval for µ will include the value 0. Page 1

2 4. The mean area µ of the several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for µ are A) H0: µ = 1250 and Ha: µ B) H0: µ = 1250 and Ha: µ < C) H0: µ = 1250 and Ha: µ > D) not able to be specified without knowing the size of the sample used by the engineer. 5. In formulating hypotheses for a statistical test of significance, the null hypothesis is often A) a statement of no effect or no difference. B) the probability of observing the data you actually obtained. C) a statement that the data are all 0. D) Is the mean height for all adult American males between the ages of 18 and 21 now over 6 feet? If the population of all adult American males between the ages of 18 and 21 has mean height of µ feet and standard deviation σ feet, to answer this question one would test which of the following null and alternative hypotheses? A) H0: µ = 6 vs. Ha: µ > 6 B) H0: µ = 6 vs. Ha: µ < 6 C) H0: µ = 6 vs. Ha: µ 6 D) H0: µ = 6 vs. Ha: µ = 6 ± x, assuming our sample size is n. 7. In a statistical test of hypotheses, we say the data are statistically significant at level α if A) α = B) α is small. C) the P-value is less than α. D) the P-value is larger than α. Page 2

3 8. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) µ and standard deviation σ = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand give a mean of x = Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses H0: µ = 1.5, Ha: µ > 1.5 at the 5% significance level. You conclude A) that H0 should be rejected. B) that H0 should not be rejected. C) that Ha should be rejected. D) there is a 5% chance that the null hypothesis is true. 9. The level of calcium in the blood of healthy young adults follows a normal distribution with mean µ = 10 milligrams per deciliter and standard deviation σ = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is x = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this, test the hypotheses H0: µ = 10, Ha: µ < 10. The P-value of your test is A) less than B) C) D) greater than We test the null hypothesis H0: µ = 10 and the alternative Ha: µ < 10, for a normal population with σ = 4. A random sample of 16 observations is drawn from the 1 population and we find the sample mean of these observations is = 12. The P-value is 3 closest to A) B) C) D) Page 3

4 11. In the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican. A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed. Let p represent the proportion of the population of all adults over the age of 65 in the city who plan to vote Republican in the next presidential election. In terms of p, the researcher should test which of the following null and alternative hypotheses? A) H0: p = 0.47 vs. Ha: p > 0.47 B) H0: p = 0.47 vs. Ha: p 0.47 C) H0: p = 0.47 vs. Ha: p < 0.47 D) H0: p = 0.47 vs. Ha: p = 0.47 ± 0.03, because 0.03 is the margin of error for most polls. 12. Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper and pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time µ is changed by vigorous exercise, so you have a random sample of nine employees of your company (that you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. You compute the average time x that it takes these employees to complete the maze and test the hypotheses H0: µ = 30, Ha: µ 30. You find that the results are significant at the 5% level. You may also conclude A) the test would also be significant at the 10% level. B) the test would also be significant at the 1% level. C) both of the above. D) none of the above. Page 4

Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

Section 8.2-8.5 Null and Alternative Hypotheses... The null hypothesis,, is a statement that the value of a population parameter is equal to some claimed value. :=0.5 The alternative hypothesis,, is the

Intro to Hypothesis Tests Solutions STAT-UB.0103 Statistics for Business Control and Regression Models Confidence Intervals (Review) 1. Each year, construction contractors and equipment distributors from

Chapter 9, Part A Hypothesis Tests Slide 1 Learning objectives 1. Understand how to develop Null and Alternative Hypotheses 2. Understand Type I and Type II Errors 3. Able to do hypothesis test about population

Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

7 Hypothesis testing - one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X

Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

Third Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notesheet. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems

HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,

Hypothesis Testing Introduction Hypothesis: A conjecture about the distribution of some random variables. A hypothesis can be simple or composite. A simple hypothesis completely specifies the distribution.

3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely

Chapter 11-12 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data

Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide

Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested

Chapter 7 - Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the

125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability

Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the

1. Which statement is not true about confidence intervals? A. A confidence interval is an interval of values computed from sample data that is likely to include the true population value. B. An approximate

Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for

CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

Lecture 10 Hypothesis Testing A hypothesis is a conjecture about the distribution of some random variables. For example, a claim about the value of a parameter of the statistical model. There are two types

Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

Hypothesis Testing --- One Mean A hypothesis is simply a statement that something is true. Typically, there are two hypotheses in a hypothesis test: the null, and the alternative. Null Hypothesis The hypothesis

Name: Class: Date: Confidence Intervals and Hypothesis Testing Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The librarian at the Library of Congress

9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis. 1) Which could be the null hypothesis for the true proportion

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

AMS 5 HYPOTHESIS TESTING Hypothesis Testing Was it due to chance, or something else? Decide between two hypotheses that are mutually exclusive on the basis of evidence from observations. Test of Significance

Name: Date: 1. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 90% confidence interval for

Chapter III Testing Hypotheses R (Introduction) A statistical hypothesis is an assumption about a population parameter This assumption may or may not be true The best way to determine whether a statistical

How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some

Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property

Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

Chapter 9 Review Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

Wording of Final Conclusion Slide 1 8.3: Assumptions for Testing Slide 2 Claims About Population Means 1) The sample is a simple random sample. 2) The value of the population standard deviation σ is known

Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus

STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

Statistics 641 - EXAM II - 1999 through 2003 December 1, 1999 I. (40 points ) Place the letter of the best answer in the blank to the left of each question. (1) In testing H 0 : µ 5 vs H 1 : µ > 5, the

1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.

HYPOTHESIS TESTING AND TYPE I AND TYPE II ERROR Hypothesis is a conjecture (an inferring) about one or more population parameters. Null Hypothesis (H 0 ) is a statement of no difference or no relationship

Chapter 7 TEST OF HYPOTHESIS In a certain perspective, we can view hypothesis testing just like a jury in a court trial. In a jury trial, the null hypothesis is similar to the jury making a decision of

Chapter 7 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number

HYPOTHESIS TESTING III: POPULATION PROPORTIONS, ETC. HYPOTHESIS TESTS OF POPULATION PROPORTIONS Purpose: to determine whether the proportion in the population with some characteristic is or is not equal

Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) 1. Which of the following symbols represents a population parameter? a. SD b. σ c. r d. 0 2. If you drew all possible

Intro to Significance Tests Name Hr For the following pairs, indicate whether they are legitimate hypotheses and why. 1. 2. 3. 4. For each situation, state the null and alternate hypothesis. (Define your

Comparing means! Tests with one categorical and one numerical variable Paired vs. sample comparisons! Goal: to compare the mean of a numerical variable for different groups. Paired comparisons allow us

Chapter 1 Hypothesis Testing Principles of Hypothesis Testing tests for one sample case 1 Statistical Hypotheses They are defined as assertion or conjecture about the parameter or parameters of a population,

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

The Normal distribution The normal probability distribution is the most common model for relative frequencies of a quantitative variable. Bell-shaped and described by the function f(y) = 1 2σ π e{ 1 2σ

Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics